Linear Representations and Isospectrality with Boundary Conditions

Details Linear Representations and Isospectrality with Boundary Conditions Linear Representations and Isospectrality with Boundary Conditions

2008-06-05

arxiv.org/abs/0806.1042v3

Journal of Geometric Analysis: Volume 20, Issue 2 (2010), Page 439.

Mathematics

Spectral Theory

Revised in response to referee's report

Scientific paper

10.1007/s12220-009-9115-6

We present a method for constructing families of isospectral systems, using linear representations of finite groups. We focus on quantum graphs, for which we give a complete treatment. However, the method presented can be applied to other systems such as manifolds and two-dimensional drums. This is demonstrated by reproducing some known isospectral drums, and new examples are obtained as well. In particular, Sunada's method is a special case of the one presented.

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